1FaMAF - CIEM, Ciudad Universitaria, 5000 Cordoba, Argentina 2Let G be a compact connected semisimple Lie group endowed with a bi-invariant Riemannian metric. We prove that maximal singular unit vector fields on G are minimal, that is, they are critical points of the volume functional on unit vector fields on G. Besides, we give a lower bound for the number of nonequivalent minimal unit vector fields on G. 3[
Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 457-464
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Marcos Salvai. On the Volume of Unit Vector Fields on a Compact Semisimple Lie Group. Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 457-464. http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a8/
@article{JOLT_2003_13_2_a8,
author = {Marcos Salvai},
title = {On the {Volume} of {Unit} {Vector} {Fields} on a {Compact} {Semisimple} {Lie} {Group}},
journal = {Journal of Lie Theory},
pages = {457--464},
year = {2003},
volume = {13},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a8/}
}
TY - JOUR
AU - Marcos Salvai
TI - On the Volume of Unit Vector Fields on a Compact Semisimple Lie Group
JO - Journal of Lie Theory
PY - 2003
SP - 457
EP - 464
VL - 13
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a8/
ID - JOLT_2003_13_2_a8
ER -
%0 Journal Article
%A Marcos Salvai
%T On the Volume of Unit Vector Fields on a Compact Semisimple Lie Group
%J Journal of Lie Theory
%D 2003
%P 457-464
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a8/
%F JOLT_2003_13_2_a8
Let G be a compact connected semisimple Lie group endowed with a bi-invariant Riemannian metric. We prove that maximal singular unit vector fields on G are minimal, that is, they are critical points of the volume functional on unit vector fields on G. Besides, we give a lower bound for the number of nonequivalent minimal unit vector fields on G.
